

partial def fact : Nat → Nat
| 0     => 1
| (n+1) => (n+1)*fact n

#eval fact 10
#eval fact 100

theorem tst1 : fact 10 = 3628800 :=
nativeRefl! (fact 10)

theorem tst2 : fact 100 = 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 :=
nativeRefl! (fact 100)

theorem tst3 : decide (10000000000000000 < 200000000000000000000) = true :=
nativeRefl! (decide (10000000000000000 < 200000000000000000000))

theorem tst4 : 10000000000000000 < 200000000000000000000 :=
ofDecideEqTrue (nativeRefl! (decide (10000000000000000 < 200000000000000000000)))

theorem tst5 : 10000000000000000 < 200000000000000000000 :=
nativeDecide!

theorem tst6 : 10000000000000000 < 200000000000000000000 :=
let h₁ := (nativeDecide! : 10000000000000000 < 10000000000000010)
let h₂ := (nativeDecide! : 10000000000000010 < 200000000000000000000)
Nat.ltTrans h₁ h₂

theorem tst7 : 10000000000000000 < 200000000000000000000 :=
decide!

theorem tst8 : 10000000000000000 < 200000000000000000000 :=
let h₁ := (decide! : 10000000000000000 < 10000000000000010)
let h₂ := (decide! : 10000000000000010 < 200000000000000000000)
Nat.ltTrans h₁ h₂

theorem tst9 : 10000000000000000 < 200000000000000000000 :=
decide!

theorem tst10 : 10000000000000000 < 200000000000000000000 :=
nativeDecide!
